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Scale Problems (scale + problem)
Kinds of Scale Problems Selected AbstractsAnalytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002J. T. Chen Abstract For a plane elasticity problem, the boundary integral equation approach has been shown to yield a non-unique solution when geometry size is equal to a degenerate scale. In this paper, the degenerate scale problem in the boundary element method (BEM) is analytically studied using the method of stress function. For the elliptic domain problem, the numerical difficulty of the degenerate scale can be solved by using the hypersingular formulation instead of using the singular formulation in the dual BEM. A simple example is shown to demonstrate the failure using the singular integral equations of dual BEM. It is found that the degenerate scale also depends on the Poisson's ratio. By employing the hypersingular formulation in the dual BEM, no degenerate scale occurs since a zero eigenvalue is not embedded in the influence matrix for any case. Copyright © 2002 John Wiley & Sons, Ltd. [source] A fast implementation of the FETI-DP method: FETI-DP-RBS-LNA and applications on large scale problems with localized non-linearitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005Jun Sun Abstract As parallel and distributed computing gradually becomes the computing standard for large scale problems, the domain decomposition method (DD) has received growing attention since it provides a natural basis for splitting a large problem into many small problems, which can be submitted to individual computing nodes and processed in a parallel fashion. This approach not only provides a method to solve large scale problems that are not solvable on a single computer by using direct sparse solvers but also gives a flexible solution to deal with large scale problems with localized non-linearities. When some parts of the structure are modified, only the corresponding subdomains and the interface equation that connects all the subdomains need to be recomputed. In this paper, the dual,primal finite element tearing and interconnecting method (FETI-DP) is carefully investigated, and a reduced back-substitution (RBS) algorithm is proposed to accelerate the time-consuming preconditioned conjugate gradient (PCG) iterations involved in the interface problems. Linear,non-linear analysis (LNA) is also adopted for large scale problems with localized non-linearities based on subdomain linear,non-linear identification criteria. This combined approach is named as the FETI-DP-RBS-LNA algorithm and demonstrated on the mechanical analyses of a welding problem. Serial CPU costs of this algorithm are measured at each solution stage and compared with that from the IBM Watson direct sparse solver and the FETI-DP method. The results demonstrate the effectiveness of the proposed computational approach for simulating welding problems, which is representative of a large class of three-dimensional large scale problems with localized non-linearities. Copyright © 2005 John Wiley & Sons, Ltd. [source] A-scalability and an integrated computational technology and framework for non-linear structural dynamics.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Part 2: Implementation aspects, parallel performance results Abstract An integrated framework and computational technology is described that addresses the issues to foster absolute scalability (A-scalability) of the entire transient duration of the simulations of implicit non-linear structural dynamics of large scale practical applications on a large number of parallel processors. Whereas the theoretical developments and parallel formulations were presented in Part 1, the implementation, validation and parallel performance assessments and results are presented here in Part 2 of the paper. Relatively simple numerical examples involving large deformation and elastic and elastoplastic non-linear dynamic behaviour are first presented via the proposed framework for demonstrating the comparative accuracy of methods in comparison to available experimental results and/or results available in the literature. For practical geometrically complex meshes, the A-scalability of non-linear implicit dynamic computations is then illustrated by employing scalable optimal dissipative zero-order displacement and velocity overshoot behaviour time operators which are a subset of the generalized framework in conjunction with numerically scalable spatial domain decomposition methods and scalable graph partitioning techniques. The constant run times of the entire simulation of ,fixed-memory-use-per-processor' scaling of complex finite element mesh geometries is demonstrated for large scale problems and large processor counts on at least 1024 processors. Copyright © 2003 John Wiley & Sons, Ltd. [source] Analytical study and numerical experiments for degenerate scale problems in the boundary element method for two-dimensional elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2002J. T. Chen Abstract For a plane elasticity problem, the boundary integral equation approach has been shown to yield a non-unique solution when geometry size is equal to a degenerate scale. In this paper, the degenerate scale problem in the boundary element method (BEM) is analytically studied using the method of stress function. For the elliptic domain problem, the numerical difficulty of the degenerate scale can be solved by using the hypersingular formulation instead of using the singular formulation in the dual BEM. A simple example is shown to demonstrate the failure using the singular integral equations of dual BEM. It is found that the degenerate scale also depends on the Poisson's ratio. By employing the hypersingular formulation in the dual BEM, no degenerate scale occurs since a zero eigenvalue is not embedded in the influence matrix for any case. Copyright © 2002 John Wiley & Sons, Ltd. [source] Comparison of GMRES and ORTHOMIN for the black oil model on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2006Wenjun Li Abstract This paper addresses an application of ORTHOMIN and GMRES to petroleum reservoir simulation using the black oil model on unstructured grids. Comparisons between these two algorithms are presented in terms of storage and total flops per restart step. Numerical results indicate that GMRES is faster than ORTHOMIN for all tested petroleum reservoir problems, particularly for large scale problems. The control volume function approximation method is utilized in the discretization of the governing equations of the black oil model. This method can accurately approximate both the pressure and velocity in the simulation of multiphase flow in porous media, effectively reduce grid orientation effects, and be easily applied to arbitrarily shaped control volumes. It is particularly suitable for hybrid grid reservoir simulation. Copyright © 2006 John Wiley & Sons, Ltd. [source] Parallel computation of a highly nonlinear Boussinesq equation model through domain decompositionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005Khairil Irfan Sitanggang Abstract Implementations of the Boussinesq wave model to calculate free surface wave evolution in large basins are, in general, computationally very expensive, requiring huge amounts of CPU time and memory. For large scale problems, it is either not affordable or practical to run on a single PC. To facilitate such extensive computations, a parallel Boussinesq wave model is developed using the domain decomposition technique in conjunction with the message passing interface (MPI). The published and well-tested numerical scheme used by the serial model, a high-order finite difference method, is identical to that employed in the parallel model. Parallelization of the tridiagonal matrix systems included in the serial scheme is the most challenging aspect of the work, and is accomplished using a parallel matrix solver combined with an efficient data transfer scheme. Numerical tests on a distributed-memory super-computer show that the performance of the current parallel model in simulating wave evolution is very satisfactory. A linear speedup is gained as the number of processors increases. These tests showed that the CPU time efficiency of the model is about 75,90%. Copyright © 2005 John Wiley & Sons, Ltd. [source] Learning scheduling control knowledge through reinforcementsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 2 2000K. Miyashita Abstract This paper introduces a method of learning search control knowledge in schedule optimization problems through application of reinforcement learning. Reinforcement learning is an effective approach for the problem faced by the agent that learns its behavior through trial-and-error interactions with a dynamic environment. Nevertheless, reinforcement learning has a difficulty of slow convergence when applied to the problems with a large state space. The paper discusses the case-based function approximation technique, which makes reinforcement learning applicable to the large scale problems such as a job-shop scheduling problem. To show effectiveness of the approach, reinforcement learning is applied to acquire search control knowledge in repair-based schedule optimization process. Preliminary experiment results show that repair-action selection made by learned search control knowledge succeeded in improving scheduling quality efficiently. [source] Planning models for parallel batch reactors with sequence-dependent changeoversAICHE JOURNAL, Issue 9 2007Muge Erdirik-Dogan Abstract In this article we address the production planning of parallel multiproduct batch reactors with sequence-dependent changeovers, a challenging problem that has been motivated by a real-world application of a specialty chemicals business. We propose two production planning models that anticipate the impact of the changeovers in this batch processing problem. The first model is based on underestimating the effects of the changeovers that leads to an MILP problem of moderate size. The second model incorporates sequencing constraints that yield very accurate predictions, but at the expense of a larger MILP problem. To solve large scale problems in terms of number of products and reactors, or length of the time horizon, we propose a decomposition technique based on rolling horizon scheme and also a relaxation of the detailed planning model. Several examples are presented to illustrate the performance of the proposed models. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] Simulation and Measurements of Rolling Tire DynamicsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006Maik Brinkmeier The simulation of rolling tires including stationary rolling, modal analysis, excitation with roughness of road surfaces and sound radiation is presented for state of the art industrial tire models. The target of this research, part of the german project "Leiser Straßenverkehr", is the reduction of trafic noise, whereas the main source, namely the tire/road system, is investigated in contrast to other techniques like sound insulating walls. The needs and methods for the solution of the resulting large scale problems are discussed next to special properties of rotating structures, high frequency behavior of rubber material and approaches for the reduction of computational cost. For the validation of the model measurements of real tires and roads are used. These include shaker tests of the standing tire and acoustics of tires rolling on a drum. The same set,ups are applied to the simulation for the comparison of frequency response functions and sound pressure levels. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||